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<a href="_linear_s_a_g_trainer_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       Generic Stochastic Average Gradient Descent training for linear models</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \author      O. Krause</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * \date        2016</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> *</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> *</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> *</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> *</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> *</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> *</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment"> */</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_LinearSAGTrainer_H</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#define SHARK_ALGORITHMS_LinearSAGTrainer_H</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_weighted_trainer_8h.html">shark/Algorithms/Trainers/AbstractWeightedTrainer.h</a>&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;<a class="code" href="_i_parameterizable_8h.html">shark/Core/IParameterizable.h</a>&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;<a class="code" href="_linear_model_8h.html">shark/Models/LinearModel.h</a>&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_loss_8h.html" title="super class of all loss functions">shark/ObjectiveFunctions/Loss/AbstractLoss.h</a>&gt;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="preprocessor">#include &lt;<a class="code" href="_multi_nomial_distribution_8h.html">shark/Statistics/Distributions/MultiNomialDistribution.h</a>&gt;</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#include &lt;<a class="code" href="_data_view_8h.html">shark/Data/DataView.h</a>&gt;</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>{</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="keyword">namespace </span>detail{</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> InputType, <span class="keyword">class</span> LabelType&gt;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <span class="keyword">struct </span>LinearSAGTrainerBase{</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        <span class="keyword">typedef</span> AbstractWeightedTrainer&lt; LinearModel&lt;InputType&gt;,LabelType &gt; type;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>        <span class="keyword">typedef</span> AbstractLoss&lt;LabelType,RealVector&gt; LossType;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    };</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> InputType&gt;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keyword">struct </span>LinearSAGTrainerBase&lt;<a class="code hl_struct" href="structshark_1_1_multi_task_sample.html" title="Aggregation of input data and task index.">InputType</a>, unsigned int&gt;{</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keyword">typedef</span> AbstractWeightedTrainer&lt; LinearClassifier&lt;InputType&gt;, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> &gt; type;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        <span class="keyword">typedef</span> AbstractLoss&lt;unsigned int,RealVector&gt; LossType;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    };</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>}</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment"></span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">///</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">/// \brief Stochastic Average Gradient Method for training of linear models,</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">///</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">/// Given a differentiable loss function L(f, y) and a model f_j(x)= w_j^Tx+b </span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">/// this trainer solves the regularized risk minimization problem</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">/// \f[</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment">///     \min \frac{1}{2} \sum_j \frac{\lambda}{2}\|w_j\|^2 + \frac 1 {\ell} \sum_i L(y_i, f(x_i)),</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">/// \f]</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">/// where i runs over training data, j over the model outputs, and lambda &gt; 0 is the</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">/// regularization parameter. </span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment">///</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">/// The algorithm uses averaging of the algorithm to obtain a good estimate of the gradient.</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">/// Averaging is performed by summing over the last gradient value obtained for each data point.</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">/// At the beginning this estimate is far off as old gradient values are outdated, but as the</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">/// algorithm converges, this gives linear convergence on strictly convex functions</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment">/// and O(1/T) convergence on not-strictly convex functions.</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment">///</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">/// The algorithm supports classification and regresseion, dense and sparse inputs</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment">/// and weighted and unweighted datasets</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment">/// Reference:</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment">/// Schmidt, Mark, Nicolas Le Roux, and Francis Bach.</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment">/// &quot;Minimizing finite sums with the stochastic average gradient.&quot;</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment">/// arXiv preprint arXiv:1309.2388 (2013).</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">/// \ingroup supervised_trainer</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputType, <span class="keyword">class</span> LabelType&gt;</div>
<div class="foldopen" id="foldopen00091" data-start="{" data-end="};">
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html">   91</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_linear_s_a_g_trainer.html" title="Stochastic Average Gradient Method for training of linear models,.">LinearSAGTrainer</a> : <span class="keyword">public</span> detail::LinearSAGTrainerBase&lt;InputType,LabelType&gt;::type, <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_i_parameterizable.html" title="Top level interface for everything that holds parameters.">IParameterizable</a>&lt;&gt;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>{</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="classshark_1_1_abstract_weighted_trainer.html" title="Superclass of weighted supervised learning algorithms.">detail::LinearSAGTrainerBase&lt;InputType,LabelType&gt;::type</a> <a class="code hl_class" href="classshark_1_1_abstract_weighted_trainer.html" title="Superclass of weighted supervised learning algorithms.">Base</a>;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a33d1c1faf1d83e0eac1506daa718ca04">   96</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="classshark_1_1_abstract_weighted_trainer.html#ad2ad0a52ecd9ac8677df6dbf403b68b4">Base::ModelType</a> <a class="code hl_typedef" href="classshark_1_1_linear_s_a_g_trainer.html#a33d1c1faf1d83e0eac1506daa718ca04">ModelType</a>;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aa6a8809d447e593855a32e6cb3156a64">   97</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="classshark_1_1_weighted_labeled_data.html" title="Weighted data set for supervised learning.">Base::WeightedDatasetType</a> <a class="code hl_typedef" href="classshark_1_1_linear_s_a_g_trainer.html#aa6a8809d447e593855a32e6cb3156a64">WeightedDatasetType</a>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aaabdd7fe303dcafb9ec99ffd993286c3">   98</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="classshark_1_1_abstract_loss.html" title="Loss function interface.">detail::LinearSAGTrainerBase&lt;InputType,LabelType&gt;::LossType</a> <a class="code hl_typedef" href="classshark_1_1_linear_s_a_g_trainer.html#aaabdd7fe303dcafb9ec99ffd993286c3">LossType</a>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span> </div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment"></span> </div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span><span class="comment">    /// \brief Constructor</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span><span class="comment">    /// \param  loss            (sub-)differentiable loss function</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span><span class="comment">    /// \param  lambda          regularization parameter fort wo-norm regularization, 0 by default</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span><span class="comment">    /// \param  offset          whether to train with offset/bias parameter or not, default is true</span></div>
<div class="foldopen" id="foldopen00106" data-start="{" data-end="}">
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a160c3456f148c696d13aee3a0dcca402">  106</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a160c3456f148c696d13aee3a0dcca402" title="Constructor.">LinearSAGTrainer</a>(<a class="code hl_class" href="classshark_1_1_abstract_loss.html" title="Loss function interface.">LossType</a> <span class="keyword">const</span>* loss, <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838" title="Return the value of the regularization parameter lambda.">lambda</a> = 0, <span class="keywordtype">bool</span> offset = <span class="keyword">true</span>)</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    : mep_loss(loss)</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    , m_lambda(<a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838" title="Return the value of the regularization parameter lambda.">lambda</a>)</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    , m_offset(offset)</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>    , m_maxEpochs(0)</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    { }</div>
</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="comment"></span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00114" data-start="{" data-end="}">
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a14d282d2649ff7d489730833f147b2d3">  114</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a14d282d2649ff7d489730833f147b2d3" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;LinearSAGTrainer&quot;</span>; }</div>
</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    <span class="keyword">using </span><a class="code hl_function" href="classshark_1_1_abstract_weighted_trainer.html#ad35ae0b236c45b73f749285a54288e89" title="Executes the algorithm and trains a model on the given weighted data.">Base::train</a>;</div>
<div class="foldopen" id="foldopen00118" data-start="{" data-end="}">
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a6de6309b709e74361bce1b2ab83f47c6">  118</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a6de6309b709e74361bce1b2ab83f47c6" title="Executes the algorithm and trains a model on the given weighted data.">train</a>(<a class="code hl_typedef" href="classshark_1_1_linear_s_a_g_trainer.html#a33d1c1faf1d83e0eac1506daa718ca04">ModelType</a>&amp; model, <a class="code hl_class" href="classshark_1_1_weighted_labeled_data.html" title="Weighted data set for supervised learning.">WeightedDatasetType</a> <span class="keyword">const</span>&amp; dataset){</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        trainImpl(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>, model,dataset,*mep_loss);</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>    }</div>
</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    </div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment"></span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">    /// \brief Return the number of training epochs.</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">    /// A value of 0 indicates that the default of max(10, dimensionOfData) should be used.</span></div>
<div class="foldopen" id="foldopen00125" data-start="{" data-end="}">
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a1e95ff06c2b294528f1d2ef394943142">  125</a></span><span class="comment"></span>    std::size_t <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a1e95ff06c2b294528f1d2ef394943142" title="Return the number of training epochs. A value of 0 indicates that the default of max(10,...">epochs</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> m_maxEpochs; }</div>
</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment"></span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">    /// \brief Set the number of training epochs.</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">    /// A value of 0 indicates that the default of max(10, dimensionOfData) should be used.</span></div>
<div class="foldopen" id="foldopen00130" data-start="{" data-end="}">
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aadca064196d92cac8b8f23f210ce89c9">  130</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aadca064196d92cac8b8f23f210ce89c9" title="Set the number of training epochs. A value of 0 indicates that the default of max(10,...">setEpochs</a>(std::size_t value)</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>    { m_maxEpochs = value; }</div>
</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span><span class="comment"></span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span><span class="comment">    /// \brief Return the value of the regularization parameter lambda.</span></div>
<div class="foldopen" id="foldopen00135" data-start="{" data-end="}">
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838">  135</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838" title="Return the value of the regularization parameter lambda.">lambda</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> m_lambda; }</div>
</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>    <span class="comment"></span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">    /// \brief Set the value of the regularization parameter lambda.</span></div>
<div class="foldopen" id="foldopen00139" data-start="{" data-end="}">
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#ac3f3baaf33ba5056acf4799b017ea806">  139</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#ac3f3baaf33ba5056acf4799b017ea806" title="Set the value of the regularization parameter lambda.">setLambda</a>(<span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838" title="Return the value of the regularization parameter lambda.">lambda</a>)</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>    { m_lambda = <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa9cfa27f5a150ef3a701ee208961a838" title="Return the value of the regularization parameter lambda.">lambda</a>; }</div>
</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span><span class="comment"></span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span><span class="comment">    /// \brief Check whether the model to be trained should include an offset term.</span></div>
<div class="foldopen" id="foldopen00143" data-start="{" data-end="}">
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a68fcdf51001257ed05a67d42d2671c10">  143</a></span><span class="comment"></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a68fcdf51001257ed05a67d42d2671c10" title="Check whether the model to be trained should include an offset term.">trainOffset</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> m_offset; }</div>
</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>    <span class="comment"></span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span><span class="comment">    /// \brief Sets whether the model to be trained should include an offset term.</span></div>
<div class="foldopen" id="foldopen00147" data-start="{" data-end="}">
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#a5cbb50a1b75f57c7dc0fe89eb28b159b">  147</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#a5cbb50a1b75f57c7dc0fe89eb28b159b" title="Sets whether the model to be trained should include an offset term.">setTrainOffset</a>(<span class="keywordtype">bool</span> offset)</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>    { m_offset = offset;}</div>
</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span><span class="comment"></span> </div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span><span class="comment">    /// \brief Returns the vector of hyper-parameters(same as lambda)</span></div>
<div class="foldopen" id="foldopen00151" data-start="{" data-end="}">
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aa2f194a2bf0013a85e567c3802391837">  151</a></span><span class="comment"></span>    RealVector <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa2f194a2bf0013a85e567c3802391837" title="Returns the vector of hyper-parameters(same as lambda)">parameterVector</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="keyword">    </span>{</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        <span class="keywordflow">return</span> RealVector(1,m_lambda);</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    }</div>
</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment"></span> </div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">    /// \brief Sets the vector of hyper-parameters(same as lambda)</span></div>
<div class="foldopen" id="foldopen00157" data-start="{" data-end="}">
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aebbf0decaa38e3fc73a13221ec3f4a9b">  157</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aebbf0decaa38e3fc73a13221ec3f4a9b" title="Sets the vector of hyper-parameters(same as lambda)">setParameterVector</a>(RealVector <span class="keyword">const</span>&amp; newParameters)</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>    {</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(newParameters.size() == 1);</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        m_lambda = newParameters(0);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>    }</div>
</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment"></span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment">    ///\brief Returns the number of hyper-parameters.</span></div>
<div class="foldopen" id="foldopen00164" data-start="{" data-end="}">
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"><a class="line" href="classshark_1_1_linear_s_a_g_trainer.html#aa424454e6433505b2ecb93c223ae43bf">  164</a></span><span class="comment"></span>    <span class="keywordtype">size_t</span> <a class="code hl_function" href="classshark_1_1_linear_s_a_g_trainer.html#aa424454e6433505b2ecb93c223ae43bf" title="Returns the number of hyper-parameters.">numberOfParameters</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="keyword">    </span>{</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>    }</div>
</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    <span class="comment">//initializes the model in the classification case and calls iterate to train it</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    <span class="keywordtype">void</span> trainImpl(</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        random::rng_type&amp; rng,</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        <a class="code hl_class" href="classshark_1_1_linear_classifier.html" title="Basic linear classifier.">LinearClassifier&lt;InputType&gt;</a>&amp; classifier,</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        <a class="code hl_class" href="classshark_1_1_weighted_labeled_data.html" title="Weighted data set for supervised learning.">WeightedLabeledData&lt;InputType, unsigned int&gt;</a> <span class="keyword">const</span>&amp; dataset,</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        <a class="code hl_class" href="classshark_1_1_abstract_loss.html" title="Loss function interface.">AbstractLoss&lt;unsigned int,RealVector&gt;</a> <span class="keyword">const</span>&amp; loss</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>    ){</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>        <span class="comment">//initialize model</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>        std::size_t classes = <a class="code hl_function" href="group__shark__globals.html#ga1fee3b5830ae11a78109e8c0265c6569" title="Return the number of classes of a set of class labels with unsigned int label encoding.">numberOfClasses</a>(dataset);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>        <span class="keywordflow">if</span>(classes == 2) classes = 1;<span class="comment">//special case: 2D classification is always encoded by the sign of the output</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>        std::size_t dim = <a class="code hl_function" href="group__shark__globals.html#gae537f0e90beb970397cd7bb9250984e2" title="Return the input dimensionality of a labeled dataset.">inputDimension</a>(dataset);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        <span class="keyword">auto</span>&amp; model = classifier.<a class="code hl_function" href="classshark_1_1_classifier.html#adf58b2ed9969bad9828772dd23c59c02" title="Return the decision function.">decisionFunction</a>();</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        model.setStructure(dim,classes, m_offset);</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        iterate(rng, model,dataset,loss);</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>    }</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>    <span class="comment">//initializes the model in the regression case and calls iterate to train it</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> LabelT&gt;</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>    <span class="keywordtype">void</span> trainImpl(</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>        random::rng_type&amp; rng,</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        LinearModel&lt;InputType&gt;&amp; model,</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        WeightedLabeledData&lt;InputType, LabelT&gt; <span class="keyword">const</span>&amp; dataset,</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>        AbstractLoss&lt;LabelT,RealVector&gt; <span class="keyword">const</span>&amp; loss</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>    ){</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        <span class="comment">//initialize model</span></div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        std::size_t labelDim = <a class="code hl_function" href="group__shark__globals.html#ga3006553139477e356ee75cd85c190d7c" title="Return the label/output dimensionality of a labeled dataset.">labelDimension</a>(dataset);</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        std::size_t dim = <a class="code hl_function" href="group__shark__globals.html#gae537f0e90beb970397cd7bb9250984e2" title="Return the input dimensionality of a labeled dataset.">inputDimension</a>(dataset);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        model.setStructure(dim,labelDim, m_offset);</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        iterate(rng, model,dataset,loss);</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>    }</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    <span class="comment">//dense vector case is easier, mostly implemented for simple exposition of the algorithm</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>    <span class="keywordtype">void</span> iterate(</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        random::rng_type&amp; rng,</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>        LinearModel&lt;blas::vector&lt;T&gt; &gt;&amp; model,</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>        WeightedLabeledData&lt;blas::vector&lt;T&gt;, <a class="code hl_typedef" href="classshark_1_1_abstract_weighted_trainer.html#a8cc4b95c06687c88b75ea8db8187336d">LabelType</a>&gt; <span class="keyword">const</span>&amp; dataset,</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        AbstractLoss&lt;LabelType,RealVector&gt; <span class="keyword">const</span>&amp; loss</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    ){</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>        </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>        <span class="comment">//get stats of the dataset</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        DataView&lt;LabeledData&lt;InputType, LabelType&gt; <span class="keyword">const</span>&gt; data(dataset.data());</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        std::size_t ell = data.size();</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        std::size_t labelDim = model.outputShape().numElements();</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        std::size_t dim = model.inputShape().numElements();</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        </div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <span class="comment">//set number of iterations</span></div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        std::size_t iterations = m_maxEpochs * ell;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        <span class="keywordflow">if</span>(m_maxEpochs == 0)</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>            iterations = std::max(10 * ell, std::size_t(std::ceil(dim * ell)));</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        </div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <span class="comment">//picking distribution picks proportional to weight</span></div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        RealVector probabilities = <a class="code hl_function" href="namespaceshark.html#a5478d144c4c997faf5c246dd8e2f85b8" title="creates a batch from a range of inputs">createBatch</a>(dataset.weights().elements());</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>        probabilities /= sum(probabilities);</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        MultiNomialDistribution dist(probabilities);</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>            </div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <span class="comment">//variables used for the SAG loop</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        RealMatrix gradD(labelDim,ell,0); <span class="comment">// gradients of regularized loss minimization with a linear model have the form sum_i D_i*x_i. We store the last acquired estimate</span></div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        RealMatrix grad(labelDim,dim);<span class="comment">// gradient of the weight matrix.</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        RealVector gradOffset(labelDim,0); <span class="comment">//sum_i D_i, gradient estimate for the offset</span></div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        RealVector pointNorms(ell); <span class="comment">//norm of each point in the dataset</span></div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <span class="keywordflow">for</span>(std::size_t  i = 0; i != ell; ++i){</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>            pointNorms(i) = norm_sqr(data[i].input);</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        }</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <span class="comment">// preinitialize everything to prevent costly memory allocations in the loop</span></div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        RealVector f_b(labelDim, 0.0); <span class="comment">// prediction of the model</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        RealVector derivative(labelDim, 0.0); <span class="comment">//derivative of the loss</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <span class="keywordtype">double</span> L = 1; <span class="comment">// initial estimate for the lipschitz-constant</span></div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        </div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="comment">// SAG loop</span></div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>        <span class="keywordflow">for</span>(std::size_t iter = 0; iter &lt; iterations; iter++)</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        {</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>            <span class="comment">// choose data point</span></div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>            std::size_t b = dist(rng);</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>            </div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>            <span class="comment">// compute prediction</span></div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>            noalias(f_b) = prod(model.matrix(), data[b].input);</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>            <span class="keywordflow">if</span>(m_offset) noalias(f_b) += model.offset();</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            </div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            <span class="comment">// compute loss gradient</span></div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            <span class="keywordtype">double</span> currentValue = loss.evalDerivative(data[b].label, f_b, derivative);</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            </div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            <span class="comment">//update gradient (needs to be multiplied with kappa)</span></div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            noalias(grad) += probabilities(b) * outer_prod(derivative-column(gradD,b), data[b].input);</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <span class="keywordflow">if</span>(m_offset) noalias(gradOffset) += probabilities(b) *(derivative-column(gradD,b));</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            noalias(column(gradD,b)) = derivative; <span class="comment">//we got a new estimate for D of element b.</span></div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            <span class="comment">// update gradient</span></div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            <span class="keywordtype">double</span> eta = 1.0/(L+m_lambda);</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            noalias(model.matrix()) *= 1 - eta * m_lambda;<span class="comment">//2-norm regularization</span></div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="keywordflow">for</span>(std::size_t i = 0; i != labelDim; ++i){</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>                <span class="keywordflow">for</span>(std::size_t j = 0; j != dim; ++j){</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                    model.matrix()(i,j) -= eta*grad(i,j);</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>                }</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            }</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            <span class="comment">//~ noalias(model.matrix()) -= eta * grad;</span></div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <span class="keywordflow">if</span>(m_offset) noalias(model.offset()) -= eta * gradOffset;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            </div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            <span class="comment">//line-search procedure, 4.6 in the paper</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>            noalias(f_b) -= derivative/L*pointNorms(b);</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            <span class="keywordtype">double</span> newValue = loss.eval(data[b].label, f_b);</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>            <span class="keywordflow">if</span>(norm_sqr(derivative)*pointNorms(b) &gt; 1.e-8 &amp;&amp; newValue &gt; currentValue - 1/(2*L)*norm_sqr(derivative)*pointNorms(b)){</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                L *= 2;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>            }</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            L*= std::pow(2.0,-1.0/ell);<span class="comment">//allow L to slightly shrink in case our initial estimate was too large</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        }</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    }</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    </div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>    <span class="keywordtype">void</span> iterate(</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        random::rng_type&amp; rng,</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        LinearModel&lt;blas::compressed_vector&lt;T&gt; &gt;&amp; model,</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        WeightedLabeledData&lt;blas::compressed_vector&lt;T&gt;, <a class="code hl_typedef" href="classshark_1_1_abstract_weighted_trainer.html#a8cc4b95c06687c88b75ea8db8187336d">LabelType</a>&gt; <span class="keyword">const</span>&amp; dataset,</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        AbstractLoss&lt;LabelType,RealVector&gt; <span class="keyword">const</span>&amp; loss</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>    ){</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        </div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        <span class="comment">//get stats of the dataset</span></div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        DataView&lt;LabeledData&lt;InputType, LabelType&gt; <span class="keyword">const</span>&gt; data(dataset.data());</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        std::size_t ell = data.size();</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        std::size_t labelDim = model.outputSize();</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        std::size_t dim = model.inputSize();</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        </div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <span class="comment">//set number of iterations</span></div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        std::size_t iterations = m_maxEpochs * ell;</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        <span class="keywordflow">if</span>(m_maxEpochs == 0)</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>            iterations = std::max(10 * ell, std::size_t(std::ceil(dim * ell)));</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        </div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        <span class="comment">//picking distribution picks proportional to weight</span></div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        RealVector probabilities = <a class="code hl_function" href="namespaceshark.html#a5478d144c4c997faf5c246dd8e2f85b8" title="creates a batch from a range of inputs">createBatch</a>(dataset.weights().elements());</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        probabilities /= sum(probabilities);</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>        MultiNomialDistribution dist(probabilities);</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>            </div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>        <span class="comment">//variables used for the SAG loop</span></div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>        blas::matrix&lt;double,blas::column_major&gt; gradD(labelDim,ell,0); <span class="comment">// gradients of regularized loss minimization with a linear model have the form sum_i D_i*x_i. We store the last acquired estimate</span></div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>        RealMatrix grad(labelDim,dim);<span class="comment">// gradient of the weight matrix.</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        RealVector gradOffset(labelDim,0); <span class="comment">//sum_i D_i, gradient estimate for the offset</span></div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        RealVector pointNorms(ell); <span class="comment">//norm of each point in the dataset</span></div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        <span class="keywordflow">for</span>(std::size_t  i = 0; i != ell; ++i){</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>            pointNorms(i) = norm_sqr(data[i].input);</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        }</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        <span class="comment">// preinitialize everything to prevent costly memory allocations in the loop</span></div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        RealVector f_b(labelDim, 0.0); <span class="comment">// prediction of the model</span></div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        RealVector derivative(labelDim, 0.0); <span class="comment">//derivative of the loss</span></div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>        <span class="keywordtype">double</span> kappa =1; <span class="comment">//we store the matrix as kappa*model.matrix() where kappa stores the effect of the 2-norm regularisation</span></div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        <span class="keywordtype">double</span> L = 1; <span class="comment">// initial estimate for the lipschitz-constant</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        </div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <span class="comment">//just in time updating for sparse inputs.</span></div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>        <span class="comment">//we need to store a running sum of step lengths which we can then apply whenever an index got updated</span></div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>        RealVector appliedRates(dim,0.0);<span class="comment">//applied steps since the last reset for each dimension</span></div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <span class="keywordtype">double</span> stepsCumSum = 0.0;<span class="comment">// cumulative update steps</span></div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        </div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <span class="comment">// SAG loop</span></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <span class="keywordflow">for</span>(std::size_t iter = 0; iter &lt; iterations; iter++)</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        {</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>            <span class="comment">// choose data point</span></div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>            std::size_t b = dist(rng);</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>            <span class="keyword">auto</span> <span class="keyword">const</span>&amp; point = data[b];</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>            </div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>            <span class="comment">//just in time update of the previous steps for every nonzero element of point b</span></div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>            <span class="keyword">auto</span> end = point.input.end();</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>            <span class="keywordflow">for</span>(<span class="keyword">auto</span>  pos = point.input.begin(); pos != end; ++pos){</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>                std::size_t index = pos.index();</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>                noalias(column(model.matrix(),index)) -= (stepsCumSum - blas::repeat(appliedRates(index),labelDim))*column(grad,index);</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>                appliedRates(index) = stepsCumSum;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>            }</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>            </div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>            <span class="comment">// compute prediction</span></div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>            noalias(f_b) = kappa * prod(model.matrix(), point.input);</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>            <span class="keywordflow">if</span>(m_offset) noalias(f_b) += model.offset();</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>            </div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>            <span class="comment">// compute loss gradient</span></div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>            <span class="keywordtype">double</span> currentValue = loss.evalDerivative(point.label, f_b, derivative);</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>            </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>            <span class="comment">//update gradient (needs to be multiplied with kappa)</span></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>            <span class="comment">//~ noalias(grad) += probabilities(b) * outer_prod(derivative-column(gradD,b), point.input); //todo: this is slow for some reason.</span></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>            <span class="keywordflow">for</span>(std::size_t l = 0; l != derivative.size(); ++l){</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>                <span class="keywordtype">double</span> val = probabilities(b) * (derivative(l) - gradD(l,b));</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>                noalias(row(grad,l)) += val * point.input;</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>            }</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>            </div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>            <span class="keywordflow">if</span>(m_offset) noalias(gradOffset) += probabilities(b) *(derivative-column(gradD,b));</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>            noalias(column(gradD,b)) = derivative; <span class="comment">//we got a new estimate for D of element b.</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>            </div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>            <span class="comment">// update gradient</span></div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>            <span class="keywordtype">double</span> eta = 1.0/(L+m_lambda);</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>            stepsCumSum += kappa * eta;<span class="comment">//we delay update of the matrix</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>            <span class="keywordflow">if</span>(m_offset) noalias(model.offset()) -= eta * gradOffset;</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>            kappa *= 1 - eta * m_lambda;<span class="comment">//2-norm regularization</span></div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>            </div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>            <span class="comment">//line-search procedure, 4.6 in the paper</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>            noalias(f_b) -= derivative/L*pointNorms(b);</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>            <span class="keywordtype">double</span> newValue = loss.eval(point.label, f_b);</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            <span class="keywordflow">if</span>(norm_sqr(derivative)*pointNorms(b) &gt; 1.e-8 &amp;&amp; newValue &gt; currentValue - 1/(2*L)*norm_sqr(derivative)*pointNorms(b)){</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>                L *= 2;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>            }</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>            L*= std::pow(2.0,-1.0/ell);<span class="comment">//allow L to slightly shrink in case our initial estimate was too large</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>            </div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>            </div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>            <span class="comment">//every epoch we reset the internal variables for numeric stability and apply all outstanding updates</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>            <span class="comment">//this also ensures that in the last iteration all updates are applied (as iterations is a multiple of ell)</span></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>            <span class="keywordflow">if</span>((iter +1)% ell == 0){</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>                noalias(model.matrix()) -= (stepsCumSum - blas::repeat(appliedRates,labelDim))*grad;</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>                model.matrix() *= kappa;</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>                kappa = 1;</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>                stepsCumSum = 0.0;</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>                appliedRates.clear();</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>            }</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        }</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>    }</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>    </div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>    <a class="code hl_typedef" href="classshark_1_1_linear_s_a_g_trainer.html#aaabdd7fe303dcafb9ec99ffd993286c3">LossType</a> <span class="keyword">const</span>* mep_loss;                 <span class="comment">///&lt; pointer to loss function</span></div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>    <span class="keywordtype">double</span> m_lambda;                          <span class="comment">///&lt; regularization parameter</span></div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>    <span class="keywordtype">bool</span> m_offset;                            <span class="comment">///&lt; should the resulting model have an offset term?</span></div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>    std::size_t m_maxEpochs;                  <span class="comment">///&lt; number of training epochs (sweeps over the data), or 0 for default = max(10, C)</span></div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>};</div>
</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span> </div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>}</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span><span class="preprocessor">#endif</span></div>
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